Download 1 - High Point University

Forming Images with Spherical Mirrors
1) Go to our course web site (PHY 1520). Scroll down on the page and click on the
“Optics Workbench” link.
2) Click on the “Mirror” button at the bottom of the workbench and then click on the
black screen to place the mirror there. Just to the right of the mirror are two
numbers; x = __ and fl = __. Note that x is the position on the screen and that x =
0 is at the far left of the screen. As you might suspect, “fl” refers to the focal
length of the mirror.
Move the mirror until it is at a position of x = 6. Then, click on the small white
dot to the left of the mirror and drag it until fl = 2.
3) Click on the “Source” button at the top of the workbench and then click on the
black screen to place the source there. This is a source of light rays, like a small
light bulb. Move the source around on the screen and observe what happens to
the light rays. Describe what happens to the light rays after they reflect off of the
mirror.
Can you find a place where you can put the source such that the light rays reflect
directly back on themselves? How far away from the mirror is this point? Use
the coordinates in the yellow box at the bottom left of the simulation to figure this
out. Remember that the mirror is located at x = 6.
This point is called the center of curvature. The reason for this is that the mirror
is a section of a sphere. The center of curvature is where the center of that sphere
would be located if the entire sphere were present. Therefore, the distance from
the mirror to the center of curvature is the radius of this sphere.
Explain why a light rays that come from the center of curvature always reflect
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directly back on themselves. Sketch a picture of the mirror to help your
explanation. Hint: Recall that the angle of incidence is equal to the angle of
reflection.
4) Click on the source that you placed on the screen and then click on the “Clear
Active” button at the bottom of the workbench. This should remove the source
from the screen. Click on the “Beam” button at the top of the workbench and
then click on the black screen to place it there. The beam produces many parallel
rays of light. Move the beam around on the screen. Describe what happens to the
rays of light after they reflect off of the mirror.
Does it matter where you put the beam on the screen?
All rays that are parallel to the optical axis get reflected back through a single
point. This point is called the focal point. How far away from the mirror (x = 6)
is the focal point located?
The distance from the mirror to the focal point is called the focal length.
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How far is the focal point away from the center of curvature?
Formulate a rule that will allow you to find the focal length if you know the
location of the center of curvature of the mirror (the radius) and vice versa.
Check your rule with your instructor.
5) Click the “Clear active” button to remove the beam from the screen. Place a
source back on the screen. You can change the number of rays that the source
puts out by clicking on the small white dot near the source and dragging it up or
down. Make it so that there is only one light ray coming from the source. Adjust
this ray so that it leaves the source and moves parallel to the optical axis. Where
does the reflected ray cross the optical axis? Does this make sense?
If you move the source around, does this change the place where the light ray
crosses the optical axis?
6) Now, adjust the ray such that it leaves the source and moves up at an angle.
Where on the optical axis would you have to place the source such that the
reflected ray moves parallel to the optical axis? Does this make sense? Explain
why.
Does the light source have to be placed exactly at this point for the reflected ray to
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be parallel to the optical axis? Try to find a place off of the optical axis where
you can place the source such that the reflected ray is parallel. How many places
can you find?
Formulate a rule that will tell you when a light ray will be reflected parallel to the
optical axis. Check your rule with your instructor.
7) Move the source such that the light ray coming from the source strikes the center
of the mirror (the point where it intersects the optical axis).
You can measure the angle of the light rays by using the angle tool. To use it,
simply click on the black background, hold the button down, and move the mouse
around. The angle tool will appear. It places a short horizontal yellow line on the
screen, and all angles are measured with respect to this line. The angle is
displayed in the yellow box at the bottom left of the workbench.
How does the reflected ray compare with the incident ray?
Any incident ray that strikes the center of the mirror will produce a reflected ray
that has this relationship.
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8) Click the “Clear Active” button to remove the source from the screen. Click on
the “Object” button at the top of the workbench and then click on the screen to
place the object there. Think of the object as a large arrow cut out of paper or
wood. Move the object so that it is at x = 1.
There are 3 different light rays leaving the top part of the arrow and going in
different directions. Follow each of the light rays as they leave the object and
then reflect off of the mirror.
What happens to the ray that leaves the arrow moving parallel to the axis?
What happens to the ray that leaves the arrow and passes through the focal point?
What happens to the ray that leaves the arrow and hits the center of the mirror?
What happens to all three of the reflected light rays when they pass below the
optical axis?
The place where all of the reflected rays come back together is called a real image
point. All of the light rays that left the top of the object come back together to
form an image of the top of the object. The faintly drawn arrow is the image.
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How is the image different from the object?
You may wonder how the rest of the image (not just the tip of the arrow) is
formed. Leave the object on the screen, but also place a source on the screen and
adjust it so that there are only two light rays. Place this source on the center of the
object (top arrow). Do the light rays that leave this point on the object converge
at some point? If so, where?
Move the light source around to different places on the object. Where do the light
rays that leave each part of the object end up converging?
9) Clear the source off of the screen. Now, move the object back and forth along the
optical axis. Notice what happens to the image.
Where do you have to place the object to make the image the same size as the
object? How far away from the mirror is this? Is this distance familiar?
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What happens to the image if you move the object to the left of the center of
curvature? Does the image move closer to or farther away from the mirror? Does
it get bigger or smaller?
What happens to the image if you move the object to the right of the center of
curvature? Does the image move closer to or farther away from the mirror? Does
it get bigger or smaller?
What happens as you move the object closer to the focal point?
If the object is at the focal point, will the reflected rays come back together to
form a real image point? Explain why or why not.
If the object is between the focal point and the mirror, will the reflected rays come
back together to form a real image point? Explain why or why not.
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If your eye were to look at the diverging light rays coming off of the mirror,
where would it interpret the rays as having come from? Make a sketch of this
below. Show the mirror, your eye, and the light rays.
10) Where would an object have to be located for the concave mirror to form a real
image of it?
11) Where would an object have to be located for the concave mirror to form a virtual
image of it?
12) Somewhere in the classroom is a large concave mirror. Obtain the mirror and try
to find the object distance at which the image changes over from being a real
image to a virtual image. Can you use this to figure out the focal length of the
mirror?
13) Now, go back to the Optics Workbench simulation. Clear everything off the
screen. Now, add a new mirror. Set the focal length of the mirror to fl = −2 and
place the mirror at the location x = 6. Note that this makes a convex mirror (i.e. it
bulges out to the left rather than caving in).
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14) Place a source on the screen and describe what happens to the light rays that hit
the convex mirror.
15) Clear the source from the screen by clicking on the source to make it active and
then clicking the “Clear Active” button. Now, add a beam to the screen. What
happens to the light rays once they hit the mirror? Where does it look like these
reflected rays are coming from?
For a convex mirror, the reflected rays always diverge. For incoming rays that are
parallel to the optical axis, the reflected rays all appear to come from a single
point behind the mirror. This point is called the focal point. So, for a convex
mirror, the focal point is behind the mirror.
16) Remove the beam from the screen and add an object. There are 3 different light
rays leaving the top part of the arrow and going in different directions. Follow
each of the light rays as they leave the object and then reflect off of the mirror.
What happens to the ray that leaves the arrow moving parallel to the axis?
What happens to the ray that leaves the arrow headed for the focal point behind
the mirror?
What happens to the ray that leaves the arrow and hits the center of the mirror?
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Note that these three light rays never actually come together. But, if you were at
the far left of the screen looking back toward the mirror, your eye would see the
diverging rays and think that they all came from a single point. Where would this
point be?
This point would be called an image point, and because the light rays did not
actually come from that point it is called a virtual image point. So, note that this
virtual image is formed behind the mirror.
17) Now, move the object back and forth in front of the convex mirror. Is a real
image ever formed?
18) Somewhere in the room is a very large convex mirror (bulges out rather than
caves in). Look at yourself in this mirror. Move different distances away from
the mirror and observe how the image you see changes. Are you looking at a real
image or a virtual image in this mirror?
19) In the space below, write a short summary of what you have learned about
concave and convex mirrors. Be sure to describe what types of images can be
formed by each mirror and how.
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